A note on the relationships between multiple imputation, maximum likelihood and fully Bayesian methods for missing...

Area of Science:

• Statistics
• Biostatistics
• Data Science

Background:

• Missing data is a common challenge in statistical analysis.
• Model-based methods like Multiple Imputation (MI), Maximum Likelihood (ML), and Fully Bayesian (FB) are frequently used.
• Complete case analysis (CCA) is known to be unbiased and efficient when data are missing at random (MAR).

Purpose of the Study:

• To investigate the performance and relationships between MI, ML, and FB methods.
• To compare these methods with complete case analysis under MAR conditions in linear regression.
• To derive and analyze small sample and asymptotic properties of these estimation methods.

Main Methods:

• Derivation of small sample and asymptotic expressions for estimates and standard errors.
• Analysis of the relationships between estimates from MI, ML, and FB approaches.
• Application to linear regression models with MAR responses.
• Simulation study and analysis of a real-world clinical trial dataset.

Main Results:

• Estimates from MI, ML, and FB methods are asymptotically equivalent to CCA estimates under MAR in linear models.
• The study provides theoretical derivations and empirical comparisons.
• Both simulation and real data analyses support the theoretical findings.

Conclusions:

• Under MAR conditions in linear regression, MI, ML, and FB methods offer results comparable to CCA, especially asymptotically.
• Understanding the equivalence of these methods aids in choosing appropriate statistical strategies for incomplete datasets.
• The findings are validated through both simulated and empirical data from a liver cancer clinical trial.